[tvtadkhg] Poisson distribution fishing game

push a button "GO FISHING" and, perhaps after an animation, you are told how many fish you caught.

the number of fish you catch is randomly sampled from a Poisson distribution.  the point of the game is just to illustrate a pun: "poisson" is French for "fish".

Easter egg: the parameter of the Poisson distribution, lambda (or 1/lambda), encodes a secret message.  it requires many fishing trips (how many?) to estimate lambda to precision high enough to read the message.  note that, although the Poisson distribution is a discrete probability distribution, its parameter lambda may be any positive real number.

fish-catching animation could be entertaining.  perhaps every fish looks distinct, procedurally generated.  perhaps the times you catch each fish during the course of the animation realistically reflect the clumpiness of arrival times of a Poisson or binomial process.  the Poisson distribution puts no upper bound on the number of fish that can be caught, so length of animation should not be proportional to the number of fish.